超越高斯噪声：一种针对非高斯噪声似然分析的通用方法
Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with non-Gaussian Noise
AI总结：
针对非高斯噪声下似然分析受限的问题，本研究提出SLIC框架，通过扩散生成模型与朗之万采样构建数据驱动的噪声模型，生成无偏似然，并经空间望远镜真实数据验证有效。
摘要：
由于难以确定复杂、高维、非高斯且各向异性噪声的概率密度函数，似然分析通常仅限于正态分布的噪声情况。这是许多科学领域（包括天体物理学，例如宇宙微波背景、引力波、引力透镜和系外行星分析）中精密测量的主要限制。本研究提出了基于得分的似然表征（Score-based LIkelihood Characterization, SLIC）框架，该框架通过使用观测得到的一组噪声实现构建数据驱动的噪声模型，解决了这一问题。我们证明，即使存在高度非高斯的相关噪声和空间变化噪声，该方法也能生成无偏且精确的似然。我们使用扩散生成模型估计噪声概率密度相对于数据元素的梯度，结合信号物理模型的雅可比矩阵，采用朗之万采样从无偏似然中生成独立样本。我们利用哈勃空间望远镜和詹姆斯·韦布空间望远镜的真实数据验证了该方法的有效性。
英文摘要：
Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for precision measurements in many domains of science, including astrophysics, for example, for the analysis of the Cosmic Microwave Background, gravitational waves, gravitational lensing, and exoplanets. This work presents Score-based LIkelihood Characterization (SLIC), a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.
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